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A287305
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Primes that can be generated by the concatenation in base 5, in descending order, of two consecutive integers read in base 10.
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0
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5, 11, 17, 23, 29, 181, 233, 311, 337, 389, 467, 571, 3527, 3779, 4157, 4283, 4409, 4787, 5039, 5417, 5669, 6047, 6173, 6299, 6551, 6803, 7307, 7433, 7559, 7937, 8693, 8819, 9323, 10079, 10331, 10457, 10709, 11087, 11213, 11717, 11969, 12347, 12473, 13103, 13229
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OFFSET
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1,1
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LINKS
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EXAMPLE
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1 and 2 in base 5 are 1 and 2 and concat(2,1) = 21 in base 10 is 11;
6 and 7 in base 5 are 11 and 12 and concat(1211) = 1211 in base 10 is 181.
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MAPLE
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with(numtheory): P:= proc(q, h) local a, b, c, d, k, n; if q=0 then 5 else a:=convert(q+1, base, h); b:=convert(q, base, h); c:=[op(a), op(b)]; d:=0; for k from nops(c) by -1 to 1 do d:=h*d+c[k]; od; if isprime(d) then d; fi; fi; end: seq(P(i, 5), i=0..1000);
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MATHEMATICA
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With[{b = 5}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Reverse /@ Partition[Range[0, 108], 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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